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                        <h1 id="46-&#x6570;&#x5B66;&#xFF1A;&#x77E9;&#x9635;">4.6 &#x6570;&#x5B66;&#xFF1A;&#x77E9;&#x9635;</h1>
<h2 id="&#x5B66;&#x4E60;&#x76EE;&#x6807;">&#x5B66;&#x4E60;&#x76EE;&#x6807;</h2>
<ul>
<li>&#x76EE;&#x6807;<ul>
<li>&#x77E5;&#x9053;&#x4EC0;&#x4E48;&#x662F;&#x77E9;&#x9635;&#x548C;&#x5411;&#x91CF;</li>
<li>&#x77E5;&#x9053;&#x77E9;&#x9635;&#x7684;&#x52A0;&#x6CD5;,&#x4E58;&#x6CD5;</li>
<li>&#x77E5;&#x9053;&#x77E9;&#x9635;&#x7684;&#x9006;&#x548C;&#x8F6C;&#x7F6E;</li>
<li>&#x5E94;&#x7528;np.matmul&#x3001;np.dot&#x5B9E;&#x73B0;&#x77E9;&#x9635;&#x8FD0;&#x7B97;</li>
</ul>
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<hr>
<h2 id="1-&#x77E9;&#x9635;&#x548C;&#x5411;&#x91CF;">1 &#x77E9;&#x9635;&#x548C;&#x5411;&#x91CF;</h2>
<h3 id="11-&#x77E9;&#x9635;">1.1 &#x77E9;&#x9635;</h3>
<p>&#x77E9;&#x9635;&#xFF0C;&#x82F1;&#x6587;matrix&#xFF0C;<strong>&#x548C;array&#x7684;&#x533A;&#x522B;&#x77E9;&#x9635;&#x5FC5;&#x987B;&#x662F;2&#x7EF4;&#x7684;&#xFF0C;&#x4F46;&#x662F;array&#x53EF;&#x4EE5;&#x662F;&#x591A;&#x7EF4;&#x7684;&#x3002;</strong></p>
<p>&#x5982;&#x56FE;:&#x8FD9;&#x4E2A;&#x662F; 3&#xD7;2 &#x77E9;&#x9635;&#xFF0C;&#x5373; 3 &#x884C; 2 &#x5217;&#xFF0C;&#x5982; m &#x4E3A;&#x884C;&#xFF0C;n &#x4E3A;&#x5217;&#xFF0C;&#x90A3;&#x4E48; m&#xD7;n &#x5373; 3&#xD7;2
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>3</mn></mrow></mtd><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>5</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
\left[
 \begin{matrix}
   1 &amp; 2  \\
   3 &amp; 4  \\
   5 &amp; 6 
  \end{matrix}
  \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span>
&#x77E9;&#x9635;&#x7684;&#x7EF4;&#x6570;&#x5373;&#x884C;&#x6570;&#xD7;&#x5217;&#x6570;</p>
<p>&#x77E9;&#x9635;&#x5143;&#x7D20;(&#x77E9;&#x9635;&#x9879;):
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>3</mn></mrow></mtd><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>5</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
A = \left[
 \begin{matrix}
   1 &amp; 2  \\
   3 &amp; 4  \\
   5 &amp; 6 
  \end{matrix}
  \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">A</span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span>
Aij &#x6307;&#x7B2C; i &#x884C;&#xFF0C;&#x7B2C; j &#x5217;&#x7684;&#x5143;&#x7D20;&#x3002;</p>
<h3 id="12-&#x5411;&#x91CF;">1.2 &#x5411;&#x91CF;</h3>
<p>&#x5411;&#x91CF;&#x662F;&#x4E00;&#x79CD;&#x7279;&#x6B8A;&#x7684;&#x77E9;&#x9635;&#xFF0C;&#x8BB2;&#x4E49;&#x4E2D;&#x7684;&#x5411;&#x91CF;&#x4E00;&#x822C;&#x90FD;&#x662F;&#x5217;&#x5411;&#x91CF;&#xFF0C;&#x4E0B;&#x9762;&#x5C55;&#x793A;&#x7684;&#x5C31;&#x662F;&#x4E09;&#x7EF4;&#x5217;
&#x5411;&#x91CF;(3&#xD7;1)&#x3002;)
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>3</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
A = \left[
 \begin{matrix}
   1  \\
   2  \\
   3 
  \end{matrix}
  \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">A</span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span></p>
<h2 id="2-&#x52A0;&#x6CD5;&#x548C;&#x6807;&#x91CF;&#x4E58;&#x6CD5;">2 &#x52A0;&#x6CD5;&#x548C;&#x6807;&#x91CF;&#x4E58;&#x6CD5;</h2>
<p>&#x77E9;&#x9635;&#x7684;&#x52A0;&#x6CD5;:&#x884C;&#x5217;&#x6570;&#x76F8;&#x7B49;&#x7684;&#x53EF;&#x4EE5;&#x52A0;&#x3002;</p>
<p>&#x4F8B;:
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>3</mn></mrow></mtd><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>5</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>3</mn></mrow></mtd><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>5</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>2</mn></mrow></mtd><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>6</mn></mrow></mtd><mtd><mrow><mn>8</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn><mn>0</mn></mrow></mtd><mtd><mrow><mn>1</mn><mn>2</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
\left[
 \begin{matrix}
   1 &amp; 2  \\
   3 &amp; 4  \\
   5 &amp; 6 
  \end{matrix}
  \right] +
\left[
 \begin{matrix}
   1 &amp; 2  \\
   3 &amp; 4  \\
   5 &amp; 6 
  \end{matrix}
  \right] = 
  \left[
 \begin{matrix}
   2 &amp; 4  \\
   6 &amp; 8  \\
   10 &amp; 12 
  \end{matrix}
  \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mbin">+</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span>
&#x77E9;&#x9635;&#x7684;&#x4E58;&#x6CD5;:&#x6BCF;&#x4E2A;&#x5143;&#x7D20;&#x90FD;&#x8981;&#x4E58;&#x3002;</p>
<p>&#x4F8B;:
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mo>&#x2217;</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>3</mn></mrow></mtd><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>5</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>3</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>9</mn></mrow></mtd><mtd><mrow><mn>1</mn><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn><mn>5</mn></mrow></mtd><mtd><mrow><mn>1</mn><mn>8</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
3 *
\left[
 \begin{matrix}
   1 &amp; 2  \\
   3 &amp; 4  \\
   5 &amp; 6 
  \end{matrix}
  \right] = 
  \left[
 \begin{matrix}
   3 &amp; 6  \\
   9 &amp; 12  \\
   15 &amp; 18 
  \end{matrix}
  \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathrm">3</span><span class="mbin">&#x2217;</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">2</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">8</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span>
&#x7EC4;&#x5408;&#x7B97;&#x6CD5;&#x4E5F;&#x7C7B;&#x4F3C;&#x3002;</p>
<h2 id="3-&#x77E9;&#x9635;&#x5411;&#x91CF;&#x4E58;&#x6CD5;">3 &#x77E9;&#x9635;&#x5411;&#x91CF;&#x4E58;&#x6CD5;</h2>
<p>&#x77E9;&#x9635;&#x548C;&#x5411;&#x91CF;&#x7684;&#x4E58;&#x6CD5;&#x5982;&#x56FE;&#xFF1A;m&#xD7;n &#x7684;&#x77E9;&#x9635;&#x4E58;&#x4EE5; n&#xD7;1 &#x7684;&#x5411;&#x91CF;&#xFF0C;&#x5F97;&#x5230;&#x7684;&#x662F; m&#xD7;1 &#x7684;&#x5411;&#x91CF;</p>
<p>&#x4F8B;:
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>3</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>4</mn></mrow></mtd><mtd><mrow><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>2</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>&#x2217;</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>5</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn><mn>6</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>7</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
\left[
 \begin{matrix}
   1 &amp; 3  \\
   4 &amp; 0  \\
   2 &amp; 1 
  \end{matrix}
  \right] *
\left[
 \begin{matrix}
   1  \\
   5 
  \end{matrix}
  \right] = 
  \left[
 \begin{matrix}
   16  \\
   4 \\
   7 
  \end{matrix}
  \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">0</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mbin">&#x2217;</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-0.6099999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:0.5900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped" style="top:0em;"><span class="delimsizing size3">]</span></span></span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">6</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span></p>
<pre><code>1*1+3*5 = 16
4*1+0*5 = 4
2*1+1*5 = 7
</code></pre><p><strong>&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x9075;&#x5FAA;&#x51C6;&#x5219;&#xFF1A;</strong></p>
<p><strong>(M&#x884C;, N&#x5217;)*(N&#x884C;, L&#x5217;) = (M&#x884C;, L&#x5217;)</strong></p>
<h2 id="4-&#x77E9;&#x9635;&#x4E58;&#x6CD5;">4 &#x77E9;&#x9635;&#x4E58;&#x6CD5;</h2>
<p>&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#xFF1A;</p>
<p>m&#xD7;n &#x77E9;&#x9635;&#x4E58;&#x4EE5; n&#xD7;o &#x77E9;&#x9635;&#xFF0C;&#x53D8;&#x6210; m&#xD7;o &#x77E9;&#x9635;&#x3002;</p>
<p>&#x4E3E;&#x4F8B;&#xFF1A;&#x6BD4;&#x5982;&#x8BF4;&#x73B0;&#x5728;&#x6709;&#x4E24;&#x4E2A;&#x77E9;&#x9635; A &#x548C; B&#xFF0C;&#x90A3; &#x4E48;&#x5B83;&#x4EEC;&#x7684;&#x4E58;&#x79EF;&#x5C31;&#x53EF;&#x4EE5;&#x8868;&#x793A;&#x4E3A;&#x56FE;&#x4E2D;&#x6240;&#x793A;&#x7684;&#x5F62;&#x5F0F;&#x3002;</p>
<p><img src="images/&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x8BA1;&#x7B97;&#x8FC7;&#x7A0B;.png" alt="image-20190221092006677"></p>
<ul>
<li><h4 id="&#x7EC3;&#x4E00;&#x7EC3;">&#x7EC3;&#x4E00;&#x7EC3;</h4>
</li>
<li><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd><mtd><mrow><mn>3</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>4</mn></mrow></mtd><mtd><mrow><mn>5</mn></mrow></mtd><mtd><mrow><mn>6</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>7</mn></mrow></mtd><mtd><mrow><mn>8</mn></mrow></mtd><mtd><mrow><mn>0</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mi>B</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>2</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
A=
  \left[
   \begin{matrix}
     1 &amp; 2 &amp; 3 \\
     4 &amp; 5 &amp; 6 \\
     7 &amp; 8 &amp; 0 
    \end{matrix} 
  \right]
  B=
  \left[
   \begin{matrix}
     1 &amp; 2 &amp; 1 \\
     1 &amp; 1 &amp; 2 \\
     2 &amp; 1 &amp; 1 
    \end{matrix} 
  \right]
  </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">A</span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">5</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">3</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">6</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">0</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mord mathit" style="margin-right:0.05017em;">B</span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span></p>
<p>&#x6C42;&#x77E9;&#x9635;AB&#x7684;&#x7ED3;&#x679C;</p>
</li>
</ul>
<p>  &#x7B54;&#x6848;&#xFF1A;
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>B</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>1</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>&#x2217;</mo><mn>2</mn></mrow></mtd><mtd><mrow><mn>1</mn><mo>&#x2217;</mo><mn>2</mn><mo>+</mo><mn>2</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>&#x2217;</mo><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>&#x2217;</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>&#x2217;</mo><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>4</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>5</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>6</mn><mo>&#x2217;</mo><mn>2</mn></mrow></mtd><mtd><mrow><mn>4</mn><mo>&#x2217;</mo><mn>2</mn><mo>+</mo><mn>5</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>6</mn><mo>&#x2217;</mo><mn>1</mn></mrow></mtd><mtd><mrow><mn>4</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>5</mn><mo>&#x2217;</mo><mn>2</mn><mo>+</mo><mn>6</mn><mo>&#x2217;</mo><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>7</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>8</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>0</mn><mo>&#x2217;</mo><mn>2</mn></mrow></mtd><mtd><mrow><mn>7</mn><mo>&#x2217;</mo><mn>2</mn><mo>+</mo><mn>8</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>0</mn><mo>&#x2217;</mo><mn>1</mn></mrow></mtd><mtd><mrow><mn>7</mn><mo>&#x2217;</mo><mn>1</mn><mo>+</mo><mn>8</mn><mo>&#x2217;</mo><mn>2</mn><mo>+</mo><mn>0</mn><mo>&#x2217;</mo><mn>1</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>9</mn></mrow></mtd><mtd><mrow><mn>7</mn></mrow></mtd><mtd><mrow><mn>8</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>2</mn><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn><mn>9</mn></mrow></mtd><mtd><mrow><mn>2</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn><mn>5</mn></mrow></mtd><mtd><mrow><mn>2</mn><mn>2</mn></mrow></mtd><mtd><mrow><mn>2</mn><mn>3</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
  B=
  \left[
   \begin{matrix}
     1*1+2*1+3*2 &amp; 1*2+2*1+3*1 &amp; 1*1+2*2+3*1 \\
     4*1+5*1+6*2 &amp; 4*2+5*1+6*1 &amp; 4*1+5*2+6*1 \\
     7*1+8*1+0*2 &amp; 7*2+8*1+0*1 &amp; 7*1+8*2+0*1 
    \end{matrix} 
  \right]
  =\left[
   \begin{matrix}
     9 &amp; 7 &amp; 8 \\
     21 &amp; 19 &amp; 20 \\
     15 &amp; 22 &amp; 23 
    \end{matrix} 
  \right]
  </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.05002em;"></span><span class="strut bottom" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit" style="margin-right:0.05017em;">B</span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">5</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">6</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">8</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">5</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">6</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">8</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">3</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">4</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">5</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">6</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord mathrm">8</span><span class="mbin">&#x2217;</span><span class="mord mathrm">2</span><span class="mbin">+</span><span class="mord mathrm">0</span><span class="mbin">&#x2217;</span><span class="mord mathrm">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span><span class="mord mathrm">1</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">5</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">9</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span><span class="mord mathrm">0</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">2</span><span class="mord mathrm">3</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span></p>
<h2 id="5-&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x7684;&#x6027;&#x8D28;">5 &#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x7684;&#x6027;&#x8D28;</h2>
<p>&#x77E9;&#x9635;&#x7684;&#x4E58;&#x6CD5;&#x4E0D;&#x6EE1;&#x8DB3;&#x4EA4;&#x6362;&#x5F8B;&#xFF1A;A&#xD7;B&#x2260;B&#xD7;A</p>
<p>&#x77E9;&#x9635;&#x7684;&#x4E58;&#x6CD5;&#x6EE1;&#x8DB3;&#x7ED3;&#x5408;&#x5F8B;&#x3002;&#x5373;&#xFF1A;A&#xD7;&#xFF08;B&#xD7;C&#xFF09;=&#xFF08;A&#xD7;B&#xFF09;&#xD7;C</p>
<p>&#x5355;&#x4F4D;&#x77E9;&#x9635;&#xFF1A;&#x5728;&#x77E9;&#x9635;&#x7684;&#x4E58;&#x6CD5;&#x4E2D;&#xFF0C;&#x6709;&#x4E00;&#x79CD;&#x77E9;&#x9635;&#x8D77;&#x7740;&#x7279;&#x6B8A;&#x7684;&#x4F5C;&#x7528;&#xFF0C;&#x5982;&#x540C;&#x6570;&#x7684;&#x4E58;&#x6CD5;&#x4E2D;&#x7684; 1,&#x6211;&#x4EEC;&#x79F0; &#x8FD9;&#x79CD;&#x77E9;&#x9635;&#x4E3A;<strong>&#x5355;&#x4F4D;&#x77E9;&#x9635;</strong>&#xFF0E;&#x5B83;&#x662F;&#x4E2A;&#x65B9;&#x9635;&#xFF0C;&#x4E00;&#x822C;&#x7528; I &#x6216;&#x8005; E &#x8868;&#x793A;&#xFF0C;&#x4ECE; &#x5DE6;&#x4E0A;&#x89D2;&#x5230;&#x53F3;&#x4E0B;&#x89D2;&#x7684;&#x5BF9;&#x89D2;&#x7EBF;&#xFF08;&#x79F0;&#x4E3A;&#x4E3B;&#x5BF9;&#x89D2;&#x7EBF;&#xFF09;&#x4E0A;&#x7684;&#x5143;&#x7D20;&#x5747;&#x4E3A; 1 &#x4EE5;&#x5916;&#x5168;&#x90FD;&#x4E3A; 0&#x3002;&#x5982;&#xFF1A;</p>
<p><img src="images/&#x5355;&#x4F4D;&#x77E9;&#x9635;.png" alt="image-20190221092155366"></p>
<h2 id="6-&#x9006;&#x3001;&#x8F6C;&#x7F6E;">6 &#x9006;&#x3001;&#x8F6C;&#x7F6E;</h2>
<p>&#x77E9;&#x9635;&#x7684;&#x9006;&#xFF1A;&#x5982;&#x77E9;&#x9635; A &#x662F;&#x4E00;&#x4E2A; m&#xD7;m &#x77E9;&#x9635;&#xFF08;&#x65B9;&#x9635;&#xFF09;&#xFF0C;&#x5982;&#x679C;&#x6709;&#x9006;&#x77E9;&#x9635;&#xFF0C;&#x5219;&#xFF1A;</p>
<p>AA<sup>-1</sup> = A<sup>-1</sup>A = I</p>
<p><strong>&#x4F4E;&#x9636;&#x77E9;&#x9635;&#x6C42;&#x9006;&#x7684;&#x65B9;&#x6CD5;:</strong></p>
<p>&#x200B;    1.&#x5F85;&#x5B9A;&#x7CFB;&#x6570;&#x6CD5;</p>
<p>&#x200B;    2.&#x521D;&#x7B49;&#x53D8;&#x6362;</p>
<p>&#x77E9;&#x9635;&#x7684;&#x8F6C;&#x7F6E;&#xFF1A;&#x8BBE; A &#x4E3A; m&#xD7;n &#x9636;&#x77E9;&#x9635;&#xFF08;&#x5373; m &#x884C; n &#x5217;&#xFF09;&#xFF0C;&#x7B2C; i &#x884C; j &#x5217;&#x7684;&#x5143;&#x7D20;&#x662F; a(i,j)&#xFF0C;&#x5373;&#xFF1A;</p>
<p>A=a(i,j)</p>
<p>&#x5B9A;&#x4E49; A &#x7684;&#x8F6C;&#x7F6E;&#x4E3A;&#x8FD9;&#x6837;&#x4E00;&#x4E2A; n&#xD7;m &#x9636;&#x77E9;&#x9635; B&#xFF0C;&#x6EE1;&#x8DB3; B=a(j,i)&#xFF0C;&#x5373; b (i,j)=a (j,i)&#xFF08;B &#x7684;&#x7B2C; i &#x884C;&#x7B2C; j &#x5217;&#x5143;&#x7D20;&#x662F; A &#x7684;&#x7B2C; j &#x884C;&#x7B2C; i &#x5217;&#x5143;&#x7D20;&#xFF09;&#xFF0C;&#x8BB0; A<sup>T</sup> =B&#x3002;</p>
<p>&#x76F4;&#x89C2;&#x6765;&#x770B;&#xFF0C;&#x5C06; A &#x7684;&#x6240;&#x6709;&#x5143;&#x7D20;&#x7ED5;&#x7740;&#x4E00;&#x6761;&#x4ECE;&#x7B2C; 1 &#x884C;&#x7B2C; 1 &#x5217;&#x5143;&#x7D20;&#x51FA;&#x53D1;&#x7684;&#x53F3;&#x4E0B;&#x65B9; 45 &#x5EA6;&#x7684;&#x5C04;&#x7EBF;&#x4F5C; &#x955C;&#x9762;&#x53CD;&#x8F6C;&#xFF0C;&#x5373;&#x5F97;&#x5230; A &#x7684;&#x8F6C;&#x7F6E;&#x3002;</p>
<p>&#x4F8B;&#xFF1A;
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mi>a</mi></mrow></mtd><mtd><mrow><mi>b</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>c</mi></mrow></mtd><mtd><mrow><mi>d</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>e</mi></mrow></mtd><mtd><mrow><mi>f</mi></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mi>T</mi></msup><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mi>a</mi></mrow></mtd><mtd><mrow><mi>c</mi></mrow></mtd><mtd><mrow><mi>e</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>b</mi></mrow></mtd><mtd><mrow><mi>d</mi></mrow></mtd><mtd><mrow><mi>f</mi></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
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=
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</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.1423509999999997em;"></span><span class="strut bottom" style="height:3.6923709999999996em;vertical-align:-1.55002em;"></span><span class="base displaystyle textstyle uncramped"><span class="minner"><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">a</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">c</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">e</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-1.2099999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">b</span></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">d</span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.9049999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:-0.89502em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="msupsub"><span class="vlist"><span style="top:-1.6640199999999998em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.13889em;">T</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-0.6099999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">a</span></span></span><span style="top:0.5900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">b</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-0.6099999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">c</span></span></span><span style="top:0.5900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">d</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-0.6099999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit">e</span></span></span><span style="top:0.5900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathit" style="margin-right:0.10764em;">f</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped" style="top:0em;"><span class="delimsizing size3">]</span></span></span></span></span></span></span></p>
<h2 id="7-&#x77E9;&#x9635;&#x8FD0;&#x7B97;">7 &#x77E9;&#x9635;&#x8FD0;&#x7B97;</h2>
<p><img src="images/&#x5B66;&#x751F;&#x6210;&#x7EE9;&#x8BA1;&#x7B97;.png" alt="&#x5B66;&#x751F;&#x6210;&#x7EE9;&#x8BA1;&#x7B97;">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>8</mn><mn>0</mn></mrow></mtd><mtd><mrow><mn>8</mn><mn>6</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>2</mn></mrow></mtd><mtd><mrow><mn>8</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>5</mn></mrow></mtd><mtd><mrow><mn>7</mn><mn>8</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>9</mn><mn>0</mn></mrow></mtd><mtd><mrow><mn>9</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>6</mn></mrow></mtd><mtd><mrow><mn>8</mn><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>2</mn></mrow></mtd><mtd><mrow><mn>9</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>7</mn><mn>8</mn></mrow></mtd><mtd><mrow><mn>8</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>9</mn><mn>2</mn></mrow></mtd><mtd><mrow><mn>9</mn><mn>4</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>&#x2217;</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>7</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>3</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable><mtr><mtd><mrow><mn>8</mn><mn>4</mn><mi mathvariant="normal">.</mi><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>0</mn><mi mathvariant="normal">.</mi><mn>6</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>0</mn><mi mathvariant="normal">.</mi><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>9</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>3</mn><mi mathvariant="normal">.</mi><mn>2</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>8</mn><mn>7</mn><mi mathvariant="normal">.</mi><mn>6</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>7</mn><mn>9</mn><mi mathvariant="normal">.</mi><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>9</mn><mn>3</mn><mi mathvariant="normal">.</mi><mn>4</mn></mrow></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">
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</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:5.05997em;"></span><span class="strut bottom" style="height:9.61004em;vertical-align:-4.55007em;"></span><span class="base displaystyle textstyle uncramped"><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:3.9050499999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:2.75005em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:2.14905em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:1.54805em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:0.94705em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:0.34604999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-0.25495em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-0.85595em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-1.45695em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-2.05795em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-2.65895em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-3.90497em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-4.21em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">0</span></span></span><span style="top:-3.0100000000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">2</span></span></span><span style="top:-1.8100000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">5</span></span></span><span style="top:-0.6100000000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">0</span></span></span><span style="top:0.5900000000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">6</span></span></span><span style="top:1.7900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">2</span></span></span><span style="top:2.9900000000000007em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span><span class="mord mathrm">8</span></span></span><span style="top:4.1899999999999995em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist"><span style="top:-4.21em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">6</span></span></span><span style="top:-3.0100000000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">0</span></span></span><span style="top:-1.8100000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span><span class="mord mathrm">8</span></span></span><span style="top:-0.6100000000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">0</span></span></span><span style="top:0.5900000000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">2</span></span></span><span style="top:1.7900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">0</span></span></span><span style="top:2.9900000000000007em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">0</span></span></span><span style="top:4.1899999999999995em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">4</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:3.9050499999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:2.75005em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:2.14905em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:1.54805em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:0.94705em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:0.34604999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-0.25495em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-0.85595em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-1.45695em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-2.05795em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-2.65895em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-3.90497em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mbin">&#x2217;</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-0.6099999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">7</span></span></span><span style="top:0.5900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">3</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped" style="top:0em;"><span class="delimsizing size3">]</span></span></span><span class="mrel">=</span><span class="minner displaystyle textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:3.9050499999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A3;</span></span></span><span style="top:2.75005em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:2.14905em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:1.54805em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:0.94705em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:0.34604999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-0.25495em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-0.85595em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-1.45695em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-2.05795em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-2.65895em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A2;</span></span></span><span style="top:-3.90497em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A1;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist"><span style="top:-4.21em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">4</span><span class="mord mathrm">.</span><span class="mord mathrm">2</span></span></span><span style="top:-3.0100000000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">6</span></span></span><span style="top:-1.8100000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">1</span></span></span><span style="top:-0.6100000000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">0</span></span></span><span style="top:0.5900000000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">3</span><span class="mord mathrm">.</span><span class="mord mathrm">2</span></span></span><span style="top:1.7900000000000003em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">8</span><span class="mord mathrm">7</span><span class="mord mathrm">.</span><span class="mord mathrm">6</span></span></span><span style="top:2.9900000000000007em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">7</span><span class="mord mathrm">9</span><span class="mord mathrm">.</span><span class="mord mathrm">4</span></span></span><span style="top:4.1899999999999995em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">3</span><span class="mord mathrm">.</span><span class="mord mathrm">4</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:3.9050499999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A6;</span></span></span><span style="top:2.75005em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:2.14905em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:1.54805em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:0.94705em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:0.34604999999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-0.25495em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-0.85595em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-1.45695em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-2.05795em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-2.65895em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A5;</span></span></span><span style="top:-3.90497em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A4;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span></span></p>
<h3 id="71-&#x77E9;&#x9635;&#x4E58;&#x6CD5;api&#xFF1A;">7.1 &#x77E9;&#x9635;&#x4E58;&#x6CD5;api&#xFF1A;</h3>
<ul>
<li>np.matmul</li>
<li>np.dot</li>
</ul>
<pre><code class="lang-python"><span class="hljs-prompt">&gt;&gt;&gt; </span>a = np.array([[<span class="hljs-number">80</span>, <span class="hljs-number">86</span>],
[<span class="hljs-number">82</span>, <span class="hljs-number">80</span>],
[<span class="hljs-number">85</span>, <span class="hljs-number">78</span>],
[<span class="hljs-number">90</span>, <span class="hljs-number">90</span>],
[<span class="hljs-number">86</span>, <span class="hljs-number">82</span>],
[<span class="hljs-number">82</span>, <span class="hljs-number">90</span>],
[<span class="hljs-number">78</span>, <span class="hljs-number">80</span>],
[<span class="hljs-number">92</span>, <span class="hljs-number">94</span>]])
<span class="hljs-prompt">&gt;&gt;&gt; </span>b = np.array([[<span class="hljs-number">0.7</span>], [<span class="hljs-number">0.3</span>]])

<span class="hljs-prompt">&gt;&gt;&gt; </span>np.matmul(a, b)
array([[<span class="hljs-number">81.8</span>],
       [<span class="hljs-number">81.4</span>],
       [<span class="hljs-number">82.9</span>],
       [<span class="hljs-number">90.</span> ],
       [<span class="hljs-number">84.8</span>],
       [<span class="hljs-number">84.4</span>],
       [<span class="hljs-number">78.6</span>],
       [<span class="hljs-number">92.6</span>]])

<span class="hljs-prompt">&gt;&gt;&gt; </span>np.dot(a,b)
array([[<span class="hljs-number">81.8</span>],
       [<span class="hljs-number">81.4</span>],
       [<span class="hljs-number">82.9</span>],
       [<span class="hljs-number">90.</span> ],
       [<span class="hljs-number">84.8</span>],
       [<span class="hljs-number">84.4</span>],
       [<span class="hljs-number">78.6</span>],
       [<span class="hljs-number">92.6</span>]])
</code></pre>
<p><strong>np.matmul&#x548C;np.dot&#x7684;&#x533A;&#x522B;:</strong></p>
<p>&#x4E8C;&#x8005;&#x90FD;&#x662F;&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x3002;
np.matmul&#x4E2D;&#x7981;&#x6B62;&#x77E9;&#x9635;&#x4E0E;&#x6807;&#x91CF;&#x7684;&#x4E58;&#x6CD5;&#x3002;
&#x5728;&#x77E2;&#x91CF;&#x4E58;&#x77E2;&#x91CF;&#x7684;&#x5167;&#x79EF;&#x8FD0;&#x7B97;&#x4E2D;&#xFF0C;np.matmul&#x4E0E;np.dot&#x6CA1;&#x6709;&#x533A;&#x522B;&#x3002;</p>
<h2 id="7-&#x5C0F;&#x7ED3;">7 &#x5C0F;&#x7ED3;</h2>
<ul>
<li>1.&#x77E9;&#x9635;&#x548C;&#x5411;&#x91CF;&#x3010;&#x77E5;&#x9053;&#x3011;<ul>
<li>&#x77E9;&#x9635;&#x5C31;&#x662F;&#x7279;&#x6B8A;&#x7684;&#x4E8C;&#x7EF4;&#x6570;&#x7EC4;</li>
<li>&#x5411;&#x91CF;&#x5C31;&#x662F;&#x4E00;&#x884C;&#x6216;&#x8005;&#x4E00;&#x5217;&#x7684;&#x6570;&#x636E;</li>
</ul>
</li>
<li>2.&#x77E9;&#x9635;&#x52A0;&#x6CD5;&#x548C;&#x6807;&#x91CF;&#x4E58;&#x6CD5;&#x3010;&#x77E5;&#x9053;&#x3011;<ul>
<li>&#x77E9;&#x9635;&#x7684;&#x52A0;&#x6CD5;:&#x884C;&#x5217;&#x6570;&#x76F8;&#x7B49;&#x7684;&#x53EF;&#x4EE5;&#x52A0;&#x3002;</li>
<li>&#x77E9;&#x9635;&#x7684;&#x4E58;&#x6CD5;:&#x6BCF;&#x4E2A;&#x5143;&#x7D20;&#x90FD;&#x8981;&#x4E58;&#x3002;</li>
</ul>
</li>
<li>3.&#x77E9;&#x9635;&#x548C;&#x77E9;&#x9635;(&#x5411;&#x91CF;)&#x76F8;&#x4E58; &#x3010;&#x77E5;&#x9053;&#x3011;<ul>
<li>(M&#x884C;, N&#x5217;)*(N&#x884C;, L&#x5217;) = (M&#x884C;, L&#x5217;)</li>
</ul>
</li>
<li>4.&#x77E9;&#x9635;&#x6027;&#x8D28;&#x3010;&#x77E5;&#x9053;&#x3011;<ul>
<li>&#x77E9;&#x9635;&#x4E0D;&#x6EE1;&#x8DB3;&#x4EA4;&#x6362;&#x7387;,&#x6EE1;&#x8DB3;&#x7ED3;&#x5408;&#x5F8B;</li>
</ul>
</li>
<li>5.&#x5355;&#x4F4D;&#x77E9;&#x9635;&#x3010;&#x77E5;&#x9053;&#x3011;<ul>
<li>&#x5BF9;&#x89D2;&#x7EBF;&#x90FD;&#x662F;1&#x7684;&#x77E9;&#x9635;,&#x5176;&#x4ED6;&#x4F4D;&#x7F6E;&#x90FD;&#x4E3A;0</li>
</ul>
</li>
<li>6.&#x77E9;&#x9635;&#x8FD0;&#x7B97;&#x3010;&#x638C;&#x63E1;&#x3011;<ul>
<li>np.matmul</li>
<li>np.dot</li>
<li>&#x6CE8;&#x610F;&#xFF1A;&#x4E8C;&#x8005;&#x90FD;&#x662F;&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x3002; np.matmul&#x4E2D;&#x7981;&#x6B62;&#x77E9;&#x9635;&#x4E0E;&#x6807;&#x91CF;&#x7684;&#x4E58;&#x6CD5;&#x3002; &#x5728;&#x77E2;&#x91CF;&#x4E58;&#x77E2;&#x91CF;&#x7684;&#x5167;&#x79EF;&#x8FD0;&#x7B97;&#x4E2D;&#xFF0C;np.matmul&#x4E0E;np.dot&#x6CA1;&#x6709;&#x533A;&#x522B;&#x3002;</li>
</ul>
</li>
</ul>

                    
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    var config = {"katex":{},"expandable-chapters":{},"splitter":{},"highlight":{},"search":{"maxIndexSize":1000000},"sharing":{"facebook":true,"twitter":true,"google":false,"weibo":false,"instapaper":false,"vk":false,"all":["facebook","google","twitter","weibo","instapaper"]},"fontsettings":{"theme":"white","family":"sans","size":2}};
    gitbook.start(config);
});
</script>

        
    </body>
    
</html>
